Details

sample39.0ms

Algorithm

intervals

Results

6.0ms	197×	body	80	valid
6.0ms	33×	body	2560	valid
6.0ms	116×	body	80	nan
4.0ms	27×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

43.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5002	2063

prune336.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.2b	(- (* b_2 b_2) (* a c))
7.0b	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

1339×	`times-frac`
946×	`add-sqr-sqrt`
940×	`*-un-lft-identity`
926×	`add-cube-cbrt`
749×	`prod-diff`
323×	`sqrt-prod`
210×	`distribute-rgt-neg-in`
207×	`distribute-lft-neg-in`
69×	`neg-mul-1`
60×	`div-inv`
35×	`fma-neg`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 889

Calls

4 calls:

7.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
3.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
31.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify250.0ms

Algorithm

egg-herbie

Counts

901 → 901

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1958	39839
1	5001	25884

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.3b	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
10.0b	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

73×	`times-frac`
69×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`add-cube-cbrt`
35×	`fma-neg` `prod-diff`
18×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
13×	`add-exp-log` `associate-r`
10×	`sqrt-div`
9×	`sqrt-prod` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `flip3--` `flip--`
6×	`neg-mul-1` `associate-l` `frac-sub` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `prod-exp` `log1p-expm1-u` `div-inv`
3×	`associate-*r/` `un-div-inv`
2×	`sub-neg` `diff-log` `div-exp` `cbrt-unprod` `sub-div`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `distribute-rgt-out--` `sqrt-pow1` `pow1/2` `1-exp` `div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 173

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
35.0ms	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
82.0ms	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify77.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	752	2220
1	2748	1911
2	5002	1871

prune449.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.2b	(/ (sqrt 1) (/ a (sqrt (- (* b_2 b_2) (* a c)))))
10.7b	(- (/ (- b_2) a) (/ (sqrt 1) (/ a (sqrt (- (* b_2 b_2) (* a c))))))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

13382×	`times-frac`
7539×	`add-sqr-sqrt`
7480×	`*-un-lft-identity`
7464×	`add-cube-cbrt`
5067×	`prod-diff`
4443×	`sqrt-prod`
1351×	`distribute-rgt-neg-in`
1350×	`distribute-lft-neg-in`
457×	`associate-/r/`
450×	`neg-mul-1`
424×	`sqrt-div`
396×	`div-inv`
214×	`flip3--` `flip--`
35×	`fma-neg`
24×	`associate-/r*`
20×	`difference-of-squares`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
2×	`sub-neg` `diff-log`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `clear-num` `frac-sub`

Counts

4 → 5363

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(/ (sqrt 1) (/ a (sqrt (- (* b_2 b_2) (* a c)))))
304.0ms	(- (/ (- b_2) a) (/ (sqrt 1) (/ a (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
82.0ms	(/ (sqrt 1) (/ a (sqrt (- (* b_2 b_2) (* a c)))))
83.0ms	(- (/ (- b_2) a) (/ (sqrt 1) (/ a (sqrt (- (* b_2 b_2) (* a c))))))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Algorithm

egg-herbie

Counts

5375 → 5375

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5001	362542

prune20.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.7b

regimes274.0ms

Accuracy

83.5% (4.8b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 35.0b

bsearch200.0ms

Steps

Iters	Range		Point
9	2.6683347110001497e+63	3.895668027475672e+69	1.5763246439716715e+69
9	-6.372026032033847e-139	-5.609109599303715e-148	-6.273278539774699e-139
10	-4.748004806532821e-81	-3.21055753719808e-93	-1.466065355378786e-87
8	-1.832018824537513e-72	-3.025657799658831e-77	-3.4003426496549383e-77

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

end0.0ms

sample1.0s

Algorithm

intervals

Results

205.0ms	1048×	body	2560	valid
196.0ms	5813×	body	80	valid
146.0ms	930×	body	1280	valid
98.0ms	2899×	body	80	nan
63.0ms	471×	body	640	valid
29.0ms	110×	body	5120	valid
21.0ms	226×	body	320	valid
7.0ms	115×	body	160	valid